I'm somewhat curious about this. Languages evolve and new words appear in all languages over time, but in modern Japanese, are new kanji created to fit these new words, or are the kana syllabaries always / most often used for new words?

Think about how new words are created in a living (evolving) language. Is the new word a combination of existing words which can therefore be represented by existing kanji or is it a loan word from another language which will be written using katakana?

Do you think that new kanji were created for words such as ひこうき (areoplane) and くうこう (airport) when they entered the Japanese language in relatively recent times ?

In Japanese kanji are sometimes used purely for their sound (ateji) in order to represent a new word.

Don't complain to me that people kick you when you're down. It's your own fault for lying there

It'd be too difficult to create new kanji in a practical manner because computer encodings wouldn't officially support them, so adoption of new kanji would necessarily be slow. Moreover, Japanese has very few characters in use that weren't borrowed from Chinese (although a good number of characters are simplifications or alterations of their original Chinese forms). The ones that do exist are called 国字 (kokuji; "national characters") or 和製漢字 (wasei-kanji; "made-in-Japan kanji"). There's actually a large number of them, but only a tiny fraction of them are still used today.

Usually, if the Japanese need a new word, they'll either make a new compound word out of existing kanji or they'll borrow a word from English (possibly changing the meaning in the process to better fit the concept).

As people have said, new words are either made by compounding already existing Kanji such as 携帯電話 (keitai-denwa: cell phone) and 遺伝子み組換え (idenshi-kumikae: genetic engineering) or taken from English / other languages and written in katakana: ブロッグ (buroggu: blog) and パソコン (pasokon [from pasonaru konpyuuta]computer).

Recently there has been a fad for using romaji acronyms to create new words such as KY (clueless- from 空気読めない- Kuuki Yomenai), but it seems too trendy and faddish to really last.

Word games involving making clever new kanji do exist, but they are one-shot jokes and not an integral part of the language.